Type I and type II codes over the ring \({\mathbb F}_2+u{\mathbb F}_2+u^2{\mathbb F}_2+u^3{\mathbb F}_2\)
Ankur Singh, Rahul Kumar · Ars Combinatoria · 2025
We consider a ring \(R_{u^3} = \mathbb{F}_2+u\mathbb{F}_2+u^2\mathbb{F}_2+u^3\mathbb{F}_2, u^4=0\). We discuss the structure of self-dual codes, Type I codes and Type II codes over the ring \(R_{u^3}\) in terms of the structure of their Torsion and Residue codes. We construct Type I and Type II optimal codes over the ring \(R_{u^3}\) for different lengths.